|
| 1. Irving Kristol wrote in the Wall Street Journal,
"This (a study showing all the officers in a precinct in New York are honest),
however, is rather like saying that the majority of New York City's police officers are
honest and honorable men. Of course they are. But the statement itself implies that a not
altogether insignificant minority are less than that, and the presence of such a minority
is fairly taken to constitute a rather serious problem." |
Analysis: |
|
| Kristol is using subalternation to go from an I
statement to an O statement. |
|
| Statement |
Reason |
T.V. |
| 1. Some NYC police officers
are honest men. |
given |
true |
| 2. Some NYC police officers
are not honest men. |
subcontrariety |
unknown |
|
| Kristol has made a mistake in his reasoning. |
|
| 2. C.S. Price in his The Improvement of Sight writes,
"Any strain imposed on the mind will be reflected in the eyes, and similarly anything
which rests the mind will benefit them." |
Analysis |
|
| Price is using contraposition and conversion of an A
proposition. |
|
| Statement |
Reason |
T.V. |
| 1. All mental strains are
nonbenefits to the eyes. |
given |
true |
| 2. All benefits to the eyes
are nonmental strains. |
contraposition |
true |
| 3. All nonmental strains are
benefits to the eyes. |
conversion |
unknown |
|
| Price has made an error; the truth values of the two
statements are not logically related. |
|
| 3. A. Conan Doyle implies that Watson's medical practice is
large. In Doyle's, "The Adventure of the Creeping Man," he writes, "Monday
morning found us on our way to the famous university town--an easy effort on the part of
Holmes, who had no roots to pull up, but one which involved frantic planning and hurrying
on my part, as my practice was by this time not inconsiderable." Are these statements
consistent? |
|
Analysis |
| The logical relation involved is obversion of an E
proposition. |
|
| Statement |
Reason |
TV |
| 1. No things which are my
practice are inconsiderable in size. |
given |
true |
| 2. All things which are my
practice are considerable in size. |
obversion |
true |
|
Notice that the translation, "All things which are my
practice are not inconsiderable" would be mistaken. Sometimes called the
"Sneaky O" proposition, statements of the form "All S is not P"
usually mean in part "Some S is not P." E.g., consider the
statement, "All swans are not white." The meaning is "Some swans are not
white." |
